QJEEM19Ma4b39: JEE Main 2019 Mathematics - Class 11 JEEM19Ma4b39 Solution: Let A(4, 4) and B(9, 6) be points on the parabola, y 2 = 4x.…

Question

Verified Solution • 2025–26 Session moderate

Let A(4,

-

4) and B(9, 6) be points on the parabola, y² = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of

\Delta

ACB is maximum. Then, the area (in sq. units) of

\Delta

ACB, is :

Accepted Answer

Δ A B C = \frac{1}{2} | \begin{matrix} 4 & - 4 & 1 \\ 9 & 6 & 1 \\ t^{2} & 2 t & 1 \end{matrix} |

D = 60 + 10t

-

10t²

{{d\Delta } \over {dt}} = 0 \Rightarrow t = {1 \over 2}

{{{d^2}\Delta } \over {d{t^2}}} = - 20 &lt; 0

\therefore

max at

t = {1 \over 2}

max area

\Delta = 65 - {5 \over 2}

= {{125} \over 2} = 31{1 \over 4}

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